generic · CBSE Class 12th English Medium · MATHEMATICS PART-2 · Page 24question
VECTOR ALGEBRA
Chapter 10: VECTOR ALGEBRA · MATHEMATICS PART-2 · EN medium
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| A Note In Example , one may note that although but the points A, B and C do not form the vertices of a triangle. EXERCISE . . Find the angle between two vectors with magnitudes and , respectively having . Find the angle between the vectors . Find the projection of the vector ˆ on the vector ˆ . Find the projection of the vector on the vector . Show that each of the given three vectors is a unit vector: ( ), ( ), ( ) Also, show that they are mutually perpendicular to each other. . Find , if . Evaluate the product . Find the magnitude of two vectors , having the same magnitude and such that the angle between them is o and their scalar product is . Find , if for a unit vector , . If are such that is perpendicular to , then find the value of λ . . Show that is perpendicular to , for any two nonzero vectors . If , then what can be concluded about the vector ? . If are unit vectors such that , find the value of . If either vector . But the converse need not be true. Justify your answer with an example. . If the vertices A, B, C of a triangle ABC are ( , , ), (– , , ), ( , , ), respectively, then find ∠ ABC. [ ∠ ABC is the angle between the vectors ]. . Show that the points A( , , ), B( , , ) and C( , , – ) are collinear. . Show that the vectors and k i form the vertices of a right angled triangle. . If is a nonzero vector of magnitude ‘ a ’ and λ a nonzero scalar, then λ is unit vector if (A) λ = (B) λ = – (C) a = | λ | (D) a = / | λ | . . Vector (or cross) product of two vectors In Section . , we |
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| ( – ) −− −− = − Hence ( ) ( ) ( ) Example Find a unit vector perpendicular to each of the vectors where Solution We have A vector which is perpendicular to both b is given by Now Therefore, the required unit vector is | r c c = ˆ |
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